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Computing endomorphism rings of abelian varieties of dimension two

Author: Gaetan Bisson
Journal: Math. Comp. 84 (2015), 1977-1989
MSC (2010): Primary 11Y40, 14Q15
Published electronically: January 20, 2015
MathSciNet review: 3335900
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Abstract: Generalizing a method of Sutherland and the author for elliptic cur ves we design a subexponential algorithm for computing the endomorphism rings of ordinary abelian varieties of dimension two over finite fields. Although its correctness and complexity analysis rest on several assumptions, we report on practical computations showing that it performs very well and can easily handle previously intractable cases.

Note. Some results of this paper previously appeared in the author's thesis, [Endomorphism Rings in Cryptography, Ph.D. Thesis. Eindhoven University of Technology and Institut National Polytechnique de Lorraine, 2011. ISBN: 90-386-2519-7].

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Gaetan Bisson
Affiliation: University of French Polynesia, BP6570, 98702 Faaa, French Polynesia

Received by editor(s): September 24, 2012
Received by editor(s) in revised form: October 15, 2013
Published electronically: January 20, 2015
Article copyright: © Copyright 2015 American Mathematical Society